Estimating the pressure inhomogeneity with spatially resolved ruby fluorescence measurements. [(a) and (b)] Micrographs of the sample pressure chamber, (a) loaded with a methanol:ethanol 4:1 mixture, compressed to 19.3 GPa at , and warmed back to room temperature, (b) after an initial loading to 2 GPa with helium pressure medium at room temperature. The difference in sample chamber size is entirely due to the high compressibility of helium; both gaskets were initially prepared with same diameter holes and thickness. The five ruby balls in each sample chamber were used for both pressure inhomogeneity and anisotropy studies. The white circles delineate an area of interest in diameter. (c) Variation in the five ruby peak positions around the mean for both pressure media up to 20 GPa. Error bars represent the uncertainty of individual peak positions and are only plotted for one ruby ball for the sake of clarity. The dashed lines model the range of this variation, which increases linearly with pressure and can be parameterized by a single inhomogeneity-per-unit-area ratio . The pressure scale on the top -axis represents our updated calibration described in Sec. IV.
FWHM of the ruby fluorescence peaks at for both pressure media up to . Plotted values are the average for the five measured rubies at each pressure, error bars are the deviation for the estimator, and the abscissa is the mean peak position for the five rubies. Full triangles are data from the experiments pictured in Figs. 1(a) and 1(b); empty triangles show data from a second experiment with the methanol:ethanol pressure medium, which was set up in almost the same manner as that pictured in Fig. 1(a) except that the placed five ruby balls covered a larger spatial area in the pressure chamber. The pressure scale on the top -axis represents our updated calibration described in Sec. IV.
Experimental setup and raw data from recent x-ray diffraction measurements of the CDW in chromium under pressure (Refs. 26–28). All data shown here were measured at and . (a) Micrograph of the sample chamber showing the oriented single crystal sample, as well as Ag foil and a ruby ball used as manometers. The diamond culet, in diameter, spans the field of view. (b) Schematic of diffraction geometry showing central (211)-type lattice Bragg peak surrounded by six CDW satellite peaks, each of which is removed from the central peak by a distance . [(c) and (d)] Rocking curve and radial scans through a (211)-type lattice Bragg peak. [(e)–(j)] scans through the six surrounding CDW peaks. Count rates are normalized to that of the lattice peak. The x-ray energy was 20.000 keV.
Rocking curves of a (211)-type lattice Bragg peak recorded during an x-ray diffraction measurement of the CDW in chromium under pressure (Refs. 26–28). Sample micrograph appears in Fig. 3(a); the peak shown in Fig. 3(c) also belongs to this series. The pressure was increased from 3.2 to 9.9 GPa in situ at in a methanol:ethanol pressure medium.
Comparison of line shapes of x-ray powder diffraction and ruby fluorescence under pressure. (a) High resolution x-ray (111) powder diffraction peaks from Ag, measured at Sector 4-ID-D of the Advanced Photon Source at for pressures 0 to 15.8 GPa. (b) Ruby fluorescence lines corresponding to the pressure series shown in (a). The silver diffraction scans are not limited by the instrument resolution (0.0085° FWHM); the ruby fluorescence measurements are not limited by the instrument resolution (0.22 nm FWHM) above 4 GPa.
Measured silver lattice constant vs peak of ruby fluorescence. Solid red circles: data taken with the psi-circle diffractometer at 4-ID-D, using vertical detector slits at a distance 1.3 m along the arm from the sample. Solid purple squares: data taken at 11-ID-C, using a Si(220) single crystal analyzer. The silver lattice constants were calculated by a -weighted average of five measured diffraction orders. Measurement uncertainties are smaller than the symbol size unless shown. The solid line is a guide to the eye.
Ruby pressure scale at . Pressure was calculated using the silver bulk modulus 108.84 GPa and the one-parameter Birch EOS. The linear fit (solid red line) up to 15.8 GPa gives the calibration for the ruby line at . For comparison we also plot an updated calibration of ruby at room T [blue long dashed line; Eq. (26) of Ref. 10 with ], as well as an early nonlinear calibration, with and (black short dashed line, Ref. 8), which was established for a wide pressure range below 80 GPa at room T.
Estimation of pressure anisotropy in a diamond anvil cell at . [(a)–(c)] Lattice constant measured at each diffraction order is plotted against for pressures at 0, 14.6, and 15.8 GPa, respectively. The last two are the highest pressure points in our Ag lattice measurement. (d) Plot of slope vs P. (e) Plot of deviatoric stress as a function of pressure. Note that most measured values are less than a variation from zero, and that there is no apparent pressure dependence. We estimate the pressure anisotropy to be .
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